chemia - Studia

OMEGA POLYNOMIAL FOR NANOSTRUCTURES DESIGNED BY (P 4 ) k Le OPERATIONS
Figure 4. 3D-vue of Le(P 4 (Do)) 2 ); v=960 ; (left) and Le(P 4 (Ico)) 2 ); v=960 ; (right)
ENERGETIC STABILITY
The calculations reported here were done at PM3 level of theory
and serve only as arguments for the topological description of the interesting
cages built up by Le((P 4 (M)) k ) sequence of operations. Data, for the smallest
representatives of this series (Figure 5) are listed in Table 1; for comparison,
data for C 60 , are also given.
Le(P 4 (T)) Le(P 4 (C)) Le(P 4 (Do))
Figure 5. The smallest cages built up by Le((P 4 (M)) k ).
It can be seen that the proposed cages show a moderate stability (by
the values of heat of formation per number of atoms HF/N and HOMO-LUMO
gap HLGAP), lower than that of C 60 , the reference structure in nanoscience [1].
Regarding aromaticity, even C 60 shows a low value of the geometrybased
HOMA (harmonic oscillator model of aromaticity) index [11-13]; the new
cages appear as anti-aromatic and this result is in agreement with the massive
presence in structure of anti-aromatic faces f 4 and f 8 , along with some aromatic
f 6 and f 10 (cf. Hückel theory) [14-16].
Table 1. Data for structures built up by (P 4 ) k Le and C 60 ; heat of formation per number
of atoms HF/N; HOMO-LUMO gap HLGAP; point group symmetry Sym
Name N HF/N HLGAP Sym. HOMA POAV1
atoms (kcal/mol) (eV)
1 Le(P 4 (T)) 48 24.386 5.948 O h -0.871 9.457
2 Le(P 4 (C)) 96 20.633 5.917 O h -0.868 4.831
3 Le(P 4 (Do)) 240 19.597 6.047 I h -0.879 2.067
4 C 60 60 13.514 6.596 I h
0.169 8.257
227